Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation

Abstract

This paper systematically investigates the Lie group analysis method of the time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions of the time-fractional (RLW) equation are obtained. It is shown that the governing equation can be transformed into a fractional ordinary differential equation with a new independent variable, where the fractional derivatives are in Erdèlyi–Kober sense. Furthermore, the explicit analytic solutions of the time-fractional (RLW) equation are obtained using the power series expansion method. Finally, some graphical features were presented to give a visual interpretation of the solutions.

Exploring the Exact Solution of the Space-Fractional Stochastic Regularized Long Wave Equation: A Bifurcation Approach

“…Like most differential equations, the RLW has been generalized using different types of fractional derivatives, and methods to solve such generalizations were investigated [28][29][30].…”

On Analytical Solution of Time-Fractional Biological Population Model by means of Generalized Integral Transform with Their Uniqueness and Convergence Analysis

“…Numerous efficient and comprehensive approaches, such as the tan-cot function method [11], the Adomian decomposition method [12], the homotopy perturbation method [13], the homotopy analysis method [14], the wavelet method [15], and the Lie symmetry analysis [16], have been constructed determined by the flexibility to form complex nonlinear phenomena in diversified disciplines such as diseases, optical fibers, fluid flow, thermodynamics, electrostatics, reaction-diffusion, and plasma physics.…”

Global Existence and Uniqueness of Solution of Atangana–Baleanu Caputo Fractional Differential Equation with Nonlinear Term and Approximate Solutions

“…Owning to their ability of use in many applications, many active related theoretical areas of research have been developed with common focus: adapting existing results and methods of integer order calculus to fractional ones. Some of those various generalization that are specially developed for fractional order differential equations are existence and uniqueness of solutions [8][9][10], numerical methods of resolution [11][12][13], Lie symmetry analysis method [14][15][16], and stability of fractional system [17][18][19]. Additionally, research studies have proposed different approaches of fractional derivatives as Riemann-Liouville, Caputo, Caputo-Fabrizio, Caputo-Hadamard, Grunwald-Letnikov, and Atangana-Baleanu derivatives.…”